Well not quite.
Amendment IV
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
The question here is, is engaging in homosexual acts such a right? Was it recognised as a right at the time of the adoption of the Constitution? It's not like homosexuality sprang forth in the last half of the 20th century and so the courts have to figure out how the Constitution applies to homosexual behavior. It's existed for a long time, and the behavior has rarely been treated as a right, if ever. So where did the right come from? Was it recognize by English Common Law, or by the Constitutions of any of the then existing states or by the compacts of any of the colonies?
It's one thing to be against sodomy laws, say as bad public policy, and quite another to assert that homosexual behavior is the exercise of a Constitutionally protected right.
Yes, that was the point I was trying to make, the other point being the Supreme Court ruling seems to go further than simply finding a specific State law "un-Constitutional"...I expect I should actually read the decisions and dissents (!), but the general concensus seems to be that an across-the-board "right to privacy" has been "discovered" (or interpreted)...
As I mentioned earlier, any such "blanket decision" will surely open a huge can of worms for obvious reasons. I'm dubious that this type of a general ruling is even within the Supremes' jurisdiction; they could have made a good argument for "equal protection" (or actually the lack thereof) in overturning the state law (not to mention it is a "silly law" as Justice Thomas stated!) but instead they go with "privacy", which really is not a Constitutional right, also for obvious reasons...I wonder why?!